Thick Turbid Media Research Articles

The Resolution Matrix in Tomographic Multiplexing: Optimization of Inter-Parameter Cross-Talk, Relative Quantitation, and Localization.

We use a resolution matrix-based Bayesian framework to compare inversion methods for tomographic fluorescence lifetime multiplexing in a diffuse medium, such as biological tissue. We consider three inversion methods; an asymptotic time domain (ATD) approach, based on a multiexponential analysis of time domain data, a direct time domain (DTD) approach, which is a minimum error solution, and a cross-talk constrained time domain (CCTD) inversion, which is a solution to an optimization problem that minimizes both error and cross-talk. We compare these methods using Monte Carlo simulations and time domain fluorescence measurements with tissue-mimicking phantoms. The ATD approach provides high accuracy of relative quantitation and spatial localization of two fluorophores embedded in a 18-mm thick turbid medium, with concentration ratios of up to 1:4.25. DTD leads to significant errors in relative quantitation and localization. CCTD provides improved quantitation accuracy over DTD, and better spatial resolution compared to ATD. We present a rigorous theoretical basis for these results and provide a complete derivation of the CCTD estimator. The Bayesian analysis also leads to a formula for rapid computation of the DTD inverse operator for large-scale tomography measurements. The ATD and CCTD inversion methods provide significant advantages over DTD for accurately estimating multiple overlapping fluorophores. Time domain fluorescence tomography, using zero cross-talk estimators, can serve as a powerful tool for quantifying multiple fluorescently labeled biological processes. The Bayesian framework presented here can be applied to general multiparameter inverse problems for the quantitative estimation of multiple overlapping parameters.

Non-Gaussian Correlations between Reflected and Transmitted Intensity Patterns Emerging from Opaque Disordered Media

The propagation of monochromatic light through a scattering medium produces speckle patterns in reflection and transmission, and the apparent randomness of these patterns prevents direct imaging through thick turbid media. Yet, since elastic multiple scattering is fundamentally a linear and deterministic process, information is not lost but distributed among many degrees of freedom that can be resolved and manipulated. Here we demonstrate experimentally that the reflected and transmitted speckle patterns are correlated, even for opaque media with thickness much larger than the transport mean free path, proving that information survives the multiple scattering process and can be recovered. The existence of mutual information between the two sides of a scattering medium opens up new possibilities for the control of transmitted light without any feedback from the target side, but using only information gathered from the reflected speckle.

Experimental evaluation of the resolution and quantitative accuracy of temperature-modulated fluorescence tomography.

Previously, we reported on the spatial resolution and quantitative accuracy of temperature-modulated fluorescence tomography (TM-FT) using simulation studies. TM-FT is a novel fully integrated multimodality imaging technique that combines fluorescence diffuse optical tomography (FT) with focused ultrasound. Utilizing unique thermo-reversible fluorescent nanocapsules (ThermoDots), TM-FT provides high-resolution cross-sectional fluorescence images in thick tissue (up to 6cm). Focused ultrasound and temperature-sensitive ThermoDots are combined to provide accurate localization of these fluorescent probes and functional a priori information to constrain the conventional FT reconstruction algorithm. Our previous simulation studies evaluated the performance of TM-FT using synthetic phantoms with multiple fluorescence targets of various sizes located at different depths. In this follow-up work, we perform experimental studies to evaluate the performance of this hybrid imaging system, in particular, the effect of size, depth, and concentration of the fluorescence target. While FT alone is unable to accurately locate and resolve the fluorophore target in many cases, TM-FT is able to resolve the size and concentration of the ThermoDots within a thick turbid medium with high accuracy for all cases. The maximum error in the recovered ThermoDots concentration and target sizes with TM-FT are 12% and 25%, respectively.

All Photons Imaging Through Volumetric Scattering.

Imaging through thick highly scattering media (sample thickness ≫ mean free path) can realize broad applications in biomedical and industrial imaging as well as remote sensing. Here we propose a computational “All Photons Imaging” (API) framework that utilizes time-resolved measurement for imaging through thick volumetric scattering by using both early arrived (non-scattered) and diffused photons. As opposed to other methods which aim to lock on specific photons (coherent, ballistic, acoustically modulated, etc.), this framework aims to use all of the optical signal. Compared to conventional early photon measurements for imaging through a 15 mm tissue phantom, our method shows a two fold improvement in spatial resolution (4db increase in Peak SNR). This all optical, calibration-free framework enables widefield imaging through thick turbid media, and opens new avenues in non-invasive testing, analysis, and diagnosis.

A deep tissue fluorescence imaging system with enhanced SHG detection capabilities

We describe a novel two-photon fluorescence microscopy system capable of producing high-quality second harmonic generation (SHG) images in thick turbid media by using an innovative detection system. This novel detection system is capable of detecting photons from a very large surface area. This system has proven effective in providing images of thick turbid samples, both biological and artificial. Due to its transmission detection geometry, the system is particularly suitable for detecting SHG signals, which are generally forward directed. In this article, we present comparative data acquired simultaneously on the same sample with the forward and epidetection schemes.

Measuring the scattering coefficient of turbid media from two-photon microscopy

In this paper, we propose a new and simple method based on two-photon excitation fluorescence (TPEF) microscopy to measure the scattering coefficient µ(s) of thick turbid media. We show, from Monte Carlo simulations, that µ(s) can be derived from the axial profile of the ratio of the TPEF signals epi-collected by the confocal and the non-descanned ports of a scanning microscope, independently of the anisotropy factor g and of the absorption coefficient µ(a) of the medium. The method is validated experimentally on tissue-mimicking optical phantoms, and is shown to have potential for imaging the scattering coefficient of heterogeneous media.

Time-domain geometrical localization of point-like fluorescence inclusions in turbid media with early photon arrival times

We introduce a novel approach for localizing a plurality of discrete point-like fluorescent inclusions embedded in a thick turbid medium using time-domain measurements. The approach uses early photon information contained in measured time-of-flight distributions originating from fluorescence emission. Fluorescence time point-spread functions (FTPSFs) are acquired with ultrafast time-correlated single photon counting after short pulse laser excitation. Early photon arrival times are extracted from the FTPSFs obtained from several source-detector positions. Each source-detector measurement allows defining a geometrical locus where an inclusion is to be found. These loci take the form of ovals in 2D or ovoids in 3D. From these loci a map can be built, with the maxima thereof corresponding to positions of inclusions. This geometrical approach is supported by Monte Carlo simulations performed for biological tissue-like media with embedded fluorescent inclusions. To validate the approach, several experiments are conducted with a homogeneous phantom mimicking tissue optical properties. In the experiments, inclusions filled with indocyanine green are embedded in the phantom and the fluorescence response to a short pulse of excitation laser is recorded. With our approach, several inclusions can be localized with low millimeter positional error. Our results support the approach as an accurate, efficient, and fast method for localizing fluorescent inclusions embedded in highly turbid media mimicking biological tissues. Further Monte Carlo simulations on a realistic mouse model show the feasibility of the technique for small animal imaging.

Focused fluorescence excitation with time-reversed ultrasonically encoded light and imaging in thick scattering media

Scattering dominates light propagation in biological tissue, and therefore restricts both resolution and penetration depth in optical imaging within thick tissue. As photons travel into the diffusive regime, typically 1 mm beneath human skin, their trajectories transition from ballistic to diffusive due to the increased number of scattering events, which makes it impossible to focus, much less track, photon paths. Consequently, imaging methods that rely on controlled light illumination are ineffective in deep tissue. This problem has recently been addressed by a novel method capable of dynamically focusing light in thick scattering media via time reversal of ultrasonically encoded (TRUE) diffused light. Here, using photorefractive materials as phase conjugate mirrors, we show a direct visualization and dynamic control of optical focusing with this light delivery method, and demonstrate its application for focused fluorescence excitation and imaging in thick turbid media. These abilities are increasingly critical for understanding the dynamic interactions of light with biological matter and processes at different system levels, as well as their applications for biomedical diagnosis and therapy.

Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation

In this work, we report a novel high capacity (number of degrees of freedom) open loop adaptive optics method, termed digital optical phase conjugation (DOPC), which provides a robust optoelectronic optical phase conjugation (OPC) solution. We showed that our prototype can phase conjugate light fields with ~3.9 x 10−3 degree accuracy over a range of ~3 degrees and can phase conjugate an input field through a relatively thick turbid medium (μsl ~13). Furthermore, we employed this system to show that the reversing of random scattering in turbid media by phase conjugation is surprisingly robust and accommodating of phase errors. An OPC wavefront with significant spatial phase errors (error uniformly distributed from – π/2 to π/2) can nevertheless allow OPC reconstruction through a scattering medium with ~40% of the efficiency achieved with phase error free OPC.

Time-resolved diffusing wave spectroscopy applied to dynamic heterogeneity imaging

We report what is to our knowledge the first observation of a time-resolved diffusing wave spectroscopy (DWS) signal recorded by transillumination through a thick turbid medium: the DWS signal is measured for a fixed photon transit time, which opens the possibility of improving the spatial resolution. This technique could find biomedical applications, especially in mammography.

Light scattering and reflectance of optically heterogeneous oriented polymers

A simple approach is used to measure the reduced scattering coefficient μ′s of a thick turbid medium having a small absorption coefficient μ′a << μ′s. Based on the light reflectance measurement of semi-infinite media with a CCD camera, the shift between the centre of the incident laser beam and the centre of the diffuse background. Δx, is determined which is inversely proportional to μ′s. The experimental values of μ′s determined for (i) EPDM particles in a polypropylene matrix and (ii) the specific case of oriented PMMA domains in a polycarbonate matrix are compared with model calculations using the Lorenz-Mie theory and a simple approximation of light scattering theory by spheroidal particles. A comparison of theoretical data with parameters from image analysis of SEM pictures gives a good accord. The dependence of light scattering patterns on mutual orientation of incident light beam and of spheroidal particles is discussed.

Spatial distribution of single-photon and two-photon fluorescence light in scattering media: Monte Carlo simulation

Three-dimensional fluorescence spatial distributions under single-photon and two-photon excitation within a turbid medium are studied with Monte Carlo simulation. It is demonstrated that two-photon excitation has an advantage of producing much less fluorescence light outside the focal region compared with single-photon excitation. With the increase of the concentration of scattering particles in a turbid medium, the position of the maximum fluorescence intensity point shifts from the geometric focal region toward the medium surface. Further studies show that the optical sectioning property of two-photon fluorescence microscopy is degraded in thick turbid media or when the numerical aperture of an objective becomes low.

Light scattering and reflectance of optically heterogeneous polymers in multiple scattering regime

A simple approach is used to measure the reduced scattering coefficient μ s ′ of a thick turbid medium having a small absorption coefficient μ a ′⪡ μ s ′. Based on the light reflectance measurement of semi-infinite media by means of a CCD camera, the value of shift Δ x between the centre of the incident laser bears and the centre of the diffuse background is determined, which is inversely proportional to the μ s ′. The experimental values of μ s ′ determined for EPDM particles in a polypropylene matrix are compared with model calculations using the Lorenz-Mie theory. A comparison of theoretical data with parameters from image analysis of SEM pictures gives good accord.

Resolution improvement in microscopic imaging through turbid media based on differential polarization gating

We report a new method for microscopic imaging of an object embedded in a turbid medium, based on the differential polarization-gating mechanism. It is demonstrated that with this method, image resolution through optically thick milk suspensions can be improved by as much as 30% compared with no-gating methods. An image resolution of tens of micrometers is achieved in an optically thick turbid medium, which is approximately 10 times better than that achieved in transillumination imaging in a similar medium.

Raman Spectroscopy and Fluorescence Photon Migration for Breast Cancer Diagnosis and Imaging

We are developing optical methods based on near infrared Raman spectroscopy and fluorescence photon migration for diagnosis and localization of breast cancer. We demonstrate the ability of Raman spectroscopy to classify accurately normal, benign and malignant breast tissues, an important step in developing Raman spectroscopic needle probes as a tool for improving the accuracy of needle biopsy. We also show that photon migration imaging can be used to localize accurately small fluorescent objects imbedded in a thick turbid medium with realistic optical properties, thus demonstrating the potential of this technique for optical imaging.

Fluorescent diffuse photon density waves in homogeneous and heterogeneous turbid media: analytic solutions and applications

We present analytic solutions for fluorescent diffuse photon density waves originating from fluorophores distributed in thick turbid media. Solutions are derived for a homogeneous turbid medium containing a uniform distribution of fluorophores and for a system that is homogeneous except for the presence of a single spherical inhomogeneity Generally the inhomogeneity has fluorophore concentration, and lifetime and optical properties that differ from those of the background. The analytic solutions are verified by numerical calculations and are used to determine the fluorophore lifetime and concentration changes required for the accurate detection of inhomogeneities in biologically relevant systems. The relative sensitivities of absorption and fluorescence methods are compared.

Gigahertz photon density waves in a turbid medium: Theory and experiments.

Author(s): Fishkin, JB; Fantini, S; vandeVen, MJ; Gratton, E | Abstract: The predictions of the frequency-domain standard diffusion equation (SDE) model for light propagation in an infinite turbid medium diverge from the more complete [Formula Presented] approximation to the linear Boltzmann transport equation at intensity modulation frequencies greater than several hundred MHz. The [Formula Presented] approximation is based on keeping only the terms l=0 and l=1 in the expansion of the angular photon density in spherical harmonics, and the nomenclature [Formula Presented] approximation is used since the spherical harmonics of order l=1 can be written in terms of the first order Legendre polynomial, which is traditionally represented by the symbol [Formula Presented]. Frequency-domain data acquired in a quasi-infinite turbid medium at modulation frequencies ranging from 0.38 to 3.2 GHz using a superheterodyning microwave detection system were analyzed using expressions derived from both the [Formula Presented] aproximation equation and the SDE. This analysis shows that the [Formula Presented] approximation provides a more accurate description of the data over this range of modulation frequencies. Some researchers have claimed that the [Formula Presented] approximation predicts that a light pulse should propagate with an average speed of c/ √3 in a thick turbid medium. However, an examination of the Green’s function that we obtained from the frequency-domain [Formula Presented] approximation model indicates that a photon density wave phase velocity of c/ √3 is only asymptotically approached in a regime where the light intensity modulation frequency aproaches infinity. The Fourier transform of this frequency-domain result shows that in the time domain, the [Formula Presented] approximation predicts that only the leading edge of the pulse (i.e., the photons arriving at the detector at the earliest time) approaches a speed of c/√3. © 1996 The American Physical Society.

Two-dimensional Kerr–Fourier imaging of translucent phantoms in thick turbid media

Translucent scattering phantoms hidden inside a 5.5-cm-thick Intralipid solution were imaged as a function of phantom scattering coefficients by the use of a picosecond time- and space-gated Kerr-Fourier imaging system. A 2-mm-thick translucent phantom with a 0.1% concentration (scattering coefficient) difference from the 55-mm-thick surrounding scattering host can be distinguished at a signal level of ~10(-10) of the incidence illumination intensity.

Transmission of a pulsed polarized light beam through thick turbid media: numerical results

We present numerical results on the change in polarization state of light pulses transmitted through thick turbid media. These results were obtained with a modified version of a previous Monte Carlo code that takes into account depolarization introduced by multiple scattering. The results have shown that for scattered received power pulse shape, polarization and total received power mainly depend on the transport cross section, σ(d), of the medium. The effect of the angular field of view of the receiver or of the distance between the diffusing medium and the receiver is shown, whereas the effect of the lateral displacement of the receiver elements proves to be of minor importance. An example of measurements showed a good agreement with numerical results, indicating the adequacy of our numerical code.

Time-resolved Fourier spectrum and imaging in highly scattering media

Time and spatial-gated Fourier spectra and imaging were measured and analyzed. A picosecond Kerr-Fourier gate was used to image objects by selecting the spatial frequencies of objects illuminated by a laser pulse passing through a thick turbid medium. The earlier arriving ballistic/snake light and most of the later scattered light were spatially filtered and temporally separated to form an image. The image contrast and the signal-to-noise ratio of hidden objects in turbid media were greatly improved with the addition of Fourier spatial filtering.